What is the value of tan(arccos(0.95))-tan(arccos(0.8)) ?

The value of tan(arccos(0.95))-tan(arccos(0.8)) is (sqrt(39))/(19)-3/4

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tan(arccos(0.95))-tan(arccos(0.8))

tan (arccos (0.95)) - tan (arccos (0.8))

\frac{39}{19} - \frac{3}{4}

Decimal Notation

- 0.42131 \dots

Solution steps

tan (arccos (0.95)) - tan (arccos (0.8))

= tan (arccos (\frac{19}{20})) - tan (arccos (\frac{4}{5}))

Rewrite using trig identities:

tan (arccos (\frac{19}{20})) = \frac{1 - ( \frac{19}{20} ) ^{2}}{( \frac{19}{20} )}

Use the following identity:

tan (arccos (x)) = \frac{1 - x ^{2}}{x}

= \frac{1 - ( \frac{19}{20} ) ^{2}}{( \frac{19}{20} )}

= \frac{1 - ( \frac{19}{20} ) ^{2}}{\frac{19}{20}} - tan (arccos (\frac{4}{5}))

Simplify

= \frac{39}{19} - tan (arccos (\frac{4}{5}))

Rewrite using trig identities:

tan (arccos (\frac{4}{5})) = \frac{3}{4}

tan (arccos (\frac{4}{5}))

Rewrite using trig identities:

tan (arccos (\frac{4}{5})) = \frac{1 - ( \frac{4}{5} ) ^{2}}{( \frac{4}{5} )}

Use the following identity:

tan (arccos (x)) = \frac{1 - x ^{2}}{x}

= \frac{1 - ( \frac{4}{5} ) ^{2}}{( \frac{4}{5} )}

= \frac{1 - ( \frac{4}{5} ) ^{2}}{\frac{4}{5}}

Simplify

= \frac{3}{4}

= \frac{39}{19} - \frac{3}{4}

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What is the value of tan(arccos(0.95))-tan(arccos(0.8)) ?
The value of tan(arccos(0.95))-tan(arccos(0.8)) is (sqrt(39))/(19)-3/4